Friday, November 9, 2012

Logic Game Rule Type: Slot

This is my second post about the Zen categorization system for logic games.

Today, I'm staying within sequencing but moving on to slot rules: what they are, how to recognize them, how to diagram them, and detail their interactions with a few other rule types.

Slot rules occur in the context of a sequencing game, where the game revolves around the order in which different actors appear. Examples include games based on races, rankings, or prioritizing to-do lists.

In today's example game, we'll talk about the sequence that ingredients are added to a dish: some are spicy, some mild. There are six potential ingredients, but only five of them can be used in the dish.

In the second example, A, D, or F could go in the fifth slot.
A slot rule specifies the exact location of a single actor (the ingredients) or group (mild or spicy) in the sequence. This is noticeably different from other sequencing rules, which rarely tie down actors without requiring some deductions.  Common examples are "A is selected fifth," or "The fifth ingredient is spicy." Examples of how to diagram these two rules are shown above. Note that on its own, a group slot rule doesn't tell you which (spicy) actor takes that slot, but rather narrows down the options to only actors from that group.

Unlike most other sequencing rule types, especially trees and barriers, slot rules rarely build upon each other to allow deductions. However, to make up for this, they almost always interact with other sequencing rules and limit the ways that the other rules can be applied. We'll circle back to slot rules in posts about barriers and conditionals, but in isolation, slot rules are pretty easy to understand and apply.

Slot rules are never contained in the game's stimulus, instead appearing in the list following the stimulus. They are often one-offs, but can appear in multiples. Obviously, most games can't have too many slot rules, or else there wouldn't be room for any questions!

As an example of how slot rules can interact with min/max, free/restricted, let's flesh out the above example about the sequencing of adding spicy and mild ingredients to a dish.

In the first panel, we can draw in A directly into the fifth slot. Oh, the beautiful simplicity of slot rules!

The second slot rule is less clear about its restrictions on the game, but is definitely more powerful when you combine it with a clear understanding of min/max. Because there is a maximum of three spicy ingredients to be added to the dish, it is incredibly limiting to include two more spicy ingredients in the first and third slots: we have to use them all! Because there are only two left, we can sketch in the possibilities: only D or F can appear in either 1 or 3, and they can only appear there.

The final step is to recognize that if three slots are thus taken up with spicy ingredients, the min/max of five total ingredients means that exacly two mild ingredients will be included. This also means that one will be left out, a powerful deduction that can make an otherwise difficult sequencing game very easy to finish.

Applying the free/restricted dichotomy to this setup, A is our most restricted actor and the spicy ingredients, as a group, are more restricted than the mild: they all must appear, and only in two possible permutations (D_F_A or F_D_A), while there are six possibilities for the mild ingredients. This realization makes a huge difference when attacking could be/must be question types, and can help you shave minutes off of your logic games time.